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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Characterization of completions of unique factorization domains
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by Raymond C. Heitmann PDF
Trans. Amer. Math. Soc. 337 (1993), 379-387 Request permission

Abstract:

It is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field, a discrete valuation ring, or it has depth at least two and no element of its prime ring is a zerodivisor. It is also shown that the Normal Chain Conjecture is false and that there exist local noncatenary UFDs.
References
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 337 (1993), 379-387
  • MSC: Primary 13B35; Secondary 13C15, 13F15
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1102888-9
  • MathSciNet review: 1102888